The 17-year-old, who finished tenth in slopestyle at the world juniors last season, grabbed the headlines off fellow Brit and Sochi 2014 medal hope James Woods in Cardrona as she was among the top eight to advance.
Vincenti scored 61.20 on her first run before returning to post 66.40 on her second and settle into the top eight, led by Tiril Sjaastad Christiansen, having never previously competed at a World Cup event.
She will compete in the final in New Zealand on Sunday as will World Cup champion and world silver medallist Woods after he scored a best of 82.00 during qualifying in the men's freestyle ski slopestyle.
While Vincenti was the only Brit in her field, Woods had company in the form of Tyler Harding, Zhachary Pham and Paddy Graham in his, all of whom were making their third World Cup start.
Harding scored 74.40, Pham 52.40 and Graham 24.00 to continue what has been a positive competition so far in New Zealand for Britain, Jenny Jones taking snowboard slopestyle World Cup silver on Monday.